In this paper, the problem of connectivity assessment for an underwater random sensor network is investigated. The weighted vertex connectivity is introduced as a metric to evaluate the connectivity of the weighted expected graph of a random sensor network where the elements of the weight matrix represent the operational probability of their corresponding communication links. The proposed weighted vertex connectivity measure extends the notion of vertex connectivity to random graphs by taking into account the joint effects of the path reliability and the network robustness to node failure.
The approximate weighted vertex connectivity measure is defined subsequently as a lower bound on the introduced connectivity metric which can be computed by applying a polynomial-time shortest path algorithm. The performance of the proposed algorithms is validated by simulation.